A295106 a(n) = (1/n) times the n-th derivative of the sixth tetration of x (power tower of order 6) x^^6 at x=1.

1, 1, 3, 14, 96, 849, 8642, 102941, 1373936, 20607888, 340516992, 6173590906, 121502258688, 2583247609500, 58940269686776, 1437019737587004, 37267502536335744, 1024420897710717344, 29745405670928179392, 909702365350759274304, 29224500667382460549504

Offset: 1

Author

Alois P. Heinz, Nov 14 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..423
• Eric Weisstein's World of Mathematics, Power Tower
• Wikipedia, Knuth's up-arrow notation
• Wikipedia, Tetration

Crossrefs

Column k=6 of A295028.

Cf. A211205.

Programs

Maple

f:= proc(n) f(n):= `if`(n=0, 1, (x+1)^f(n-1)) end:
a:= n-> (n-1)!*coeff(series(f(6), x, n+1), x, n):
seq(a(n), n=1..23);

Mathematica

f[n_] := f[n] = If[n == 0, 1, (x + 1)^f[n - 1]];
a[n_] := (n - 1)!*SeriesCoefficient[f[6], {x, 0, n}];
Array[a, 23] (* Jean-François Alcover, May 31 2018, from Maple *)

Formula

a(n) = 1/n * [(d/dx)^n x^^6]_{x=1}.

a(n) = (n-1)! * [x^n] (x+1)^^6.

a(n) = 1/n * A211205(n).